Highest Common Factor of 629, 493, 421 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 629, 493, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 629, 493, 421 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 629, 493, 421 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 629, 493, 421 is 1.
HCF(629, 493, 421) = 1
HCF of 629, 493, 421 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 629, 493, 421 is 1.
Highest Common Factor of 629,493,421 is 1
Step 1: Since 629 > 493, we apply the division lemma to 629 and 493, to get
629 = 493 x 1 + 136
Step 2: Since the reminder 493 ≠ 0, we apply division lemma to 136 and 493, to get
493 = 136 x 3 + 85
Step 3: We consider the new divisor 136 and the new remainder 85, and apply the division lemma to get
136 = 85 x 1 + 51
We consider the new divisor 85 and the new remainder 51,and apply the division lemma to get
85 = 51 x 1 + 34
We consider the new divisor 51 and the new remainder 34,and apply the division lemma to get
51 = 34 x 1 + 17
We consider the new divisor 34 and the new remainder 17,and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 629 and 493 is 17
Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(85,51) = HCF(136,85) = HCF(493,136) = HCF(629,493) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 17, we apply the division lemma to 421 and 17, to get
421 = 17 x 24 + 13
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 13 and 17, to get
17 = 13 x 1 + 4
Step 3: We consider the new divisor 13 and the new remainder 4, and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 421 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(421,17) .
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Frequently Asked Questions on HCF of 629, 493, 421 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 629, 493, 421?
Answer: HCF of 629, 493, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 629, 493, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 629, 493, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.